The linear matching method for shakedown and limit analyses applied to rolling and sliding point contact problems

An understanding of the load bearing capacity of road pavements requires insight into the load levels at which incremental plastic strains occur under rolling contact. A number of authors have described solutions of this problem in terms of shakedown limits, assuming particular simple classes of plastic deformation patterns and using the upper bound shakedown theorem. In this paper we describe a general numerical technique, the Linear Matching Method, for evaluating the shakedown limit under rolling contact including surface friction where the mechanism at the shakedown limit may be described by any finite element discretization. In this way, very accurate shakedown limits may be evaluated. Comparisons are made with the semi-analytical solution of Ponter, Hearle and Johnson [PON85] for a von Mises yield condition, as a first step towards the development of such methods for pavement design.